A weighted ℓ{sub 1}-minimization approach for sparse polynomial chaos expansions
- Mechanical Engineering Department, University of Colorado, Boulder, CO 80309 (United States)
- Aerospace Engineering Sciences Department, University of Colorado, Boulder, CO 80309 (United States)
This work proposes a method for sparse polynomial chaos (PC) approximation of high-dimensional stochastic functions based on non-adapted random sampling. We modify the standard ℓ{sub 1}-minimization algorithm, originally proposed in the context of compressive sampling, using a priori information about the decay of the PC coefficients, when available, and refer to the resulting algorithm as weightedℓ{sub 1}-minimization. We provide conditions under which we may guarantee recovery using this weighted scheme. Numerical tests are used to compare the weighted and non-weighted methods for the recovery of solutions to two differential equations with high-dimensional random inputs: a boundary value problem with a random elliptic operator and a 2-D thermally driven cavity flow with random boundary condition.
- OSTI ID:
- 22314869
- Journal Information:
- Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 267; ISSN JCTPAH; ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
Similar Records
Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies
A Generalized Sampling and Preconditioning Scheme for Sparse Approximation of Polynomial Chaos Expansions